Why have camera lens protectors suddenly become a thing? I don’t think I had even heard of them before this year. The camera lenses are covered in sapphire crystal. They are very difficult to scratch (though they can be chipped if the phone is dropped since sapphire is fairly brittle). They don’t really need extra protection.
If you DO decide to add a protector, you will be degrading the image quality by definition. Leaving aside the question of adhesives, you are adding an extra layer of glass in front of the camera. When light hits that glass, some will be transmitted through and some reflected back out into the world. No glass, no matter how good quality and how many antireflective coatings it has, transmits 100% of light that hits it. So you are reducing the amount of light that reaches the sensor just by having the glass there. If the glass is bad quality, it could also reduce sharpness and lead to color shifts.
Now, if this protector has some sort of adhesive that goes on the lens, I don’t even know how bad that would make things. For sure your risk of losing sharpness goes up. The adhesive would also further reduce the amount of light reaching the sensor since there is now another layer of stuff the light has to get through.
Seriously, don’t get a lens protector. The existing sapphire is plenty strong and these poor little phone camera sensors need all the light they can get.
Since the area of the cover glass is very small and far off the actual focal range, regular adhesives or films will not significantly affect the clarity or the sharpness. Rather, what we really should care about is the flare and ghosting that mostly originate from the reflectivity of the lenses that you've mentioned. Because the key factors that play a role in making us feel that something is clear in visual are "brightness and contrast" which is susceptible to reflectivity and flares.
As energy is conserved, high reflectivity means reduced amount of light passing through, and increased amount of unintended path of light reflecting between multiple lenses to reach the sensor, resulting in ghosting or flares.
Beside the actual seven-element lenses inside, the sapphire crystal cover of the iPhone does NOT have anti-reflective coating.
What makes it worse is that sapphire crystals have higher reflectivity than regular tempered glass. And you can clearly see that the sapphire cover is evidently making the flare and ghosting worse than it could have been if it were treated with AR coating.
The reflectivity "from the adhesive to the sapphire lens" will be lower than from the air, as the air has extremely low refraction. So when the protector is properly treated with an anti-reflective coating and has high transparency, it will rather suppress the reflectance of the camera lens, thereby easing ghost and flare. Plus, lowered reflection means increased amount of light reaching the lens and the sensor!
+ Most screen protectors on the market transmit more than 95% of light, so the decrease in brightness after attachment will be negligible anyway.
You don't have to be that worried of the degrading the camera quality when putting protectors on the camera, unless you've ripped off the sapphire cover which is already that bad. There's nothing that can go worse.